The maths of ruin: why sizing matters more than edge.

Risk-of-ruin is the calculation that tells you, given your edge and your sizing, what the probability is your book hits an unrecoverable loss before it compounds.

Risk-of-ruin is the calculation that tells you, given your edge and your sizing, what the probability is your book hits an unrecoverable loss before it compounds. It's the question every trader needs an honest answer to, and one of the harder numbers to get right.

The formula in its simplest form: P(ruin) ≈ ((1 - edge)/(1 + edge))^(units of risk available).

Three inputs. Assuming a symmetric binary outcome (where wins and losses are of equal magnitude), Edge is the per-trade probability advantage (p - q) expressed as a fraction of your risk unit. Units of risk available is how many max-stop losses your book can sustain before it hits the ruin threshold. The exponent is what does the work.

Suppose your strategy has a 1% edge per trade, and you're sizing such that one full stop is 0.5% of equity. The ruin threshold is, say, a 25% drawdown. That gives you 50 units of risk available. Plug in: P(ruin) ≈ 0.99^50 / 1.01^50 ≈ 0.37.

37% chance of ruin. With a 1% edge.

Flip the sizing. Same edge, stop is 0.2% of equity. The ruin threshold of 25% gives you 125 units of risk available. P(ruin) ≈ 0.99^125 / 1.01^125 ≈ 0.083.

8% chance of ruin. Same edge. Smaller sizing. The risk-of-ruin maths collapses from 37% to 8% because you've added 75 units of risk available.

There are a few things that this calculation makes obvious:

Edge alone is meaningless without sizing context. A 2% edge sized aggressively can have higher ruin probability than a 0.5% edge sized conservatively.

The ruin threshold matters as much as the edge. If you don't know the drawdown level at which you will dismantle the strategy or stop adding to it, you don't know what you're solving for.

The calculation tends to reward smaller sizing more than a larger edge. A 50% reduction in stop size does roughly the same work for ruin probability as doubling your edge. Edge is where a trader's attention usually defaults to, but sizing is where the cheaper improvement actually lives.

What does this mean in practice?

For strategy development: every candidate strategy should run through a risk-of-ruin calculation at the proposed live sizing. If ruin probability at the proposed size is above some threshold, the sizing comes down before the strategy goes live.

For portfolio construction: the ruin calculation extends to the book level. If you're running 28 strategies, the question is whether the book hits an unrecoverable drawdown, not whether any single strategy does.

The calculation is a baseline, it's not 100%. It assumes a fixed edge, a static stop, and ruin defined as a hard threshold, but at this point precision is not the point. The point is that running the maths of ruin forces you to answer structural questions about your book that perhaps you've overlooked in your workflow. Recovery time matters as much as depth, which is why time-under-water belongs in your monthly reporting.